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  1. The study of epidemics is useful for not only understanding outbreaks and trying to limit their adverse effects, but also because epidemics are related to social phenomena such as government instability, crime, poverty, and inequality. One approach for studying epidemics is to simulate their spread through populations. In this work, we describe an integrated multi-dimensional approach to epidemic simulation, which encompasses: (i) a theoretical framework for simulation and analysis; (ii) synthetic population (digital twin) generation; (iii) (social contact) network construction methods from synthetic populations, (iv) stylized network construction methods; and (v) simulation of the evolution of a virus or disease through a social network. We describe these aspects and end with a short discussion on simulation results that inform public policy. 
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  3. Graph scan statistics have become popular for event detection in networks. This methodology involves finding connected subgraphs that maximize a certain anomaly function, but maximizing these functions is computationally hard in general. We develop a novel approach for graph scan statistics with connectivity constraints. Our algorithm Approx-MultilinearScan relies on an algebraic technique called multilinear detection, and it improves over prior methods for large networks. We also develop a Pregel-based parallel version of this algorithm in Giraph, MultilinearScanGiraph, that allows us to solve instances with over 40 million edges, which is more than one order of magnitude larger than existing methods. 
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